Level 2: Probability · Problem 26 of 87

Variance of a discrete distribution

A statistics problem from Statisticsdrill. Solve it with one answer box, with a fresh sample on every attempt and the worked steps and spreadsheet function in the answer, and it is checked the moment you submit.

The task

The number of service calls a field technician completes in a day, X, has this probability distribution: P(X = 2) = 0.05, P(X = 3) = 0.65, P(X = 4) = 0.2, P(X = 5) = 0.1. What is the variance of X? Round to 2 decimal places.

What this problem teaches

The formula: Var(X) = Σ x² P(x) - μ², with μ = Σ x P(x). Weight each squared deviation by its probability. VAR.S or VAR.P on the list of x values ignores the probabilities and gives the wrong number.

A hint if you get stuck

First find μ = Σ x P(x). Then Var(X) = Σ (x - μ)² P(x), or equivalently Σ x² P(x) - μ².